4x^2+4x+5=0

Question

4x^2+4x+5=0

helpz-q · Answer

Trying to factor by splitting the middle term

 2.1     Factoring  4x2+4x+5 

The first term is,  4x2  its coefficient is  4 .
The middle term is,  +4x  its coefficient is  4 .
The last term, "the constant", is  +5 

Step-1 : Multiply the coefficient of the first term by the constant   4 • 5 = 20 

Step-2 : Find two factors of  20  whose sum equals the coefficient of the middle term, which is   4 .

     	-20	   +   	-1	   =   	-21	
     	-10	   +   	-2	   =   	-12	
     	-5	   +   	-4	   =   	-9	
     	-4	   +   	-5	   =   	-9	
     	-2	   +   	-10	   =   	-12	
     	-1	   +   	-20	   =   	-21	
     	1	   +   	20	   =   	21	
     	2	   +   	10	   =   	12	
     	4	   +   	5	   =   	9	
     	5	   +   	4	   =   	9	
     	10	   +   	2	   =   	12	
     	20	   +   	1	   =   	21	

Observation : No two such factors can be found !! 
Conclusion : Trinomial can not be factored

Final result :

  4x2 + 4x + 5

melodyeason74 · Answer

thank you very much, that helped a bunch

helpz-q · Answer

Hi mathmale

helpz-q · Answer

I have a question for you, do you a second?

mathmale · Answer

Actually, you could apply the quadratic formula to this quadratic equation.  The q. formula will produce two roots.  Just supposing that one such root were x=2-j, then one factor of the given quadratic would be (x-2+j).

helpz-q · Answer

and math male, i did not think about that, you might be right